Helu kumumanaʻo: kumumanaʻo o ka hana

Aia i kekahi mau wehewehe o ka makahiki "kumumanaʻo o ka helu." Kekahi o ia nei i ka mea mea he kūikawā lala o ka makemakika (makemakika a oi aku), a huli aku i ka au mamuli o ka pau loa a me ka mea like me ia.

Kekahi ho'ākāka 'ana hoʻomōakaaka i keia lala o ka makemakika këia na waiwai o ka loa a me kā lākou mau hana ma kekahi wahi, i hiki.

Kekahi kānakaʻepekema i manaʻo i ke kumumanaʻo mea ai nui i ka mea e haawi aku i ka kūlike loa ka wehewehena mea hiki ole, a me oe wale mahele mai i emi ka leo theories.

E hoʻopaʻa i reliably ka wā originated i ka kumumanaʻo o ka helu, ia mea,ʻaʻole e hiki. Eia naʻe, e hoʻouka kekahi: i kēia lā i ka makahiapo, akā, i ka mea wale palapala e hōʻike ana i ka ukupanee a hiki i ka kumumanaʻo kahiko o ka nui, mea he uuku apana nahaha o ka lepo papa 1800s BC. It - He helu o no laila,-kapaia Pythagorean triples (maoli helu), he nui no a he poe elima kaha. A nui helu o triples nele ka neʻe aku lākou me mechanical koho. Ua paipai i hoihoi i loko o apparently ka pähola 'ana o ka huina ala ae nui mua ma mua o ko nā kānakaʻepekema mua manaʻo.

Ke koʻikoʻi loa, nā mea hana keaka i loko o ka ulu ana o ka pähola 'ana o ka Pythagoreans, noonoo iho la Euclid, a Diophantus, ka poʻe i noho i loko o ka Middle Ages Indians Aryabhata, Brahmagupta a me Bhaskara, a hiki hope - Fermat, Euler, Lagrange.

I ke kakahiaka nui iwakālua kenekulia helu kumumanaʻo ua o Laielohelohe i ka noonoo ana o ka makemakika geniuses me A. N. Korkin, E. I. Zolotarov, A. A. Markov, B. N. Delone, DK Faddeev, I. M. Vinogradov, G .Veyl Selberg.

? Ac? Aaioea a Wa Mamua i ka helu a me ka haʻawina o kahiko mathematicians, lawe ae la lakou i ka pähola 'ana i ka hou, nui kiekie ae kaʻilikai, e uhi ana i nā hana. Ma-hohonu, ka noiʻi, a me ka huli 'ana no ka hou hōʻike, a alakaʻi ai i ka loaʻa o ka hou pilikia, kekahi o i i ole, ua aʻo a hiki i kēia manawa. E noho hamama: Artin kuhiakau o infinitely nui primes, i ka ninau o ka mana loa helu o primes, nui no hoi na theories.

Ma keia manawa i ka papa kuhikuhiE eiiiiiaiou, a i puunaueia i helu kumumanaʻo, ke kumumanaʻo i: haʻahaʻa, nui helu o ka huikau ka helu, mākau, algebraic.

Elementary helu kumumanaʻo epa me ke ao ana o integers, me ka unuhi i ka 'ana i kūpono a me ka manaÿo mai nā lālā o ka makemakika. Fibonacci helu, uuku Fermat ka hope theorem, - i kēia mau mea i ka loa, he pono ole, ua pono-ikeia a hiki i schoolchildren manaÿo mai i kēia kumumanaʻo.

I ka kumumanaʻo o ka nui loa (a me ke kānāwai o ka nui loa) - māhele o lalo pahiki kumumanaʻo, uaʻimi mai kēlā i ka hooiaio ana i ka makemakika O ia hoʻi, (ma kekahi - ka awelika o ka manamana nui) nui hāpana o kokoke i ka manao a (i ua i kapaʻia ai kaʻimi naʻauaoʻawelike) o ka hāpana ma lalo o keʻano o ka paa hoi o ka makana.

I ka kumumanaʻo o ka huikau ka heluʻana, e hoʻokēʻai a pau nā hanana i loko o ka ole, deterministic a me ka huikau, ho'āʻo ana e hooholo i ka pahiki o ka luna 'probabilities o ka poe noonoo ole hanana. Kēia māhele nā na waiwai o conditional probabilities a me kā lākou multiplication theorem, Theorem hypotheses (pinepine kapa Bayes 'haʻilula) a pela aku.

Analytic helu kumumanaʻo, e like me ka mea hala ole oe i kona inoa, no ka mea study o makemakika mea a me ka laulā waiwai o nā kiʻina hana a me nā 'ana i kūpono o ka makemakika Ka Ikepili. Kekahi o na kumu nui kuhikuhi o keia kumumanaʻo - ka maopopo (hoʻohana luna 'Ikepili) ma luna o ka puunaue ana o Kuhina Nui helu.

Algebraic Number kumumanaʻo hana 'ana me ka nui o ko lākou mau analogues (e laʻa me, algebraic nui), Haʻawina kumumanaʻo mahele pae cohomology Dirichlet ho'āʻo etc.

Ke ano a me ka ulu ana o keia kumumanaʻo alakaʻi ho'āʻo kenekulia-kahiko e ho'āʻo Fermat ka theorem.

A hiki i ka iwakalua kenekulia, ka pähola 'ana o ka huina i manaoia he Hōʻuluʻulu' epekema, "maemae no o ka makemakika",ʻaʻole ka loaʻaʻohe mea hiki ole utilitarian noi. I kēia lā, ka mea, ua hoʻohana 'ia i loko o ka computation o cryptographic Hola Pūnaewele, ma ka helu ana i ka trajectories o ka pa alima a me ka lewa probes, iaaiey. 'Aoʻao hoʻokele waiwai, waiwai, kamepiula epekema, geology - a pau kēia mau sciences i keia la, ua hiki ole me ke kumumanaʻo o ka helu.